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90 lines
2.5 KiB
90 lines
2.5 KiB
/*
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* Copyright(C) 1999-2020 National Technology & Engineering Solutions
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* of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with
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* NTESS, the U.S. Government retains certain rights in this software.
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*
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* See packages/seacas/LICENSE for details
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*/
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#include "defs.h"
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#include <math.h>
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/* Find eigenvalues of 2x2 symmetric system by solving quadratic. */
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void evals2(double H[2][2], /* symmetric matrix for eigenvalues */
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double *eval1, /* smallest eigenvalue */
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double *eval2 /* middle eigenvalue */
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)
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{
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double M[2][2]; /* normalized version of matrix */
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double b, c; /* coefficients of cubic equation */
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double root1, root2; /* roots of quadratic */
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double xmax; /* largest matrix element */
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int i, j; /* loop counters */
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M[0][0] = M[1][0] = M[0][1] = M[1][1] = 0.0;
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xmax = 0.0;
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for (i = 0; i < 2; i++) {
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for (j = i; j < 2; j++) {
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if (fabs(H[i][j]) > xmax) {
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xmax = fabs(H[i][j]);
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}
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}
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}
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if (xmax != 0) {
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for (i = 0; i < 2; i++) {
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for (j = 0; j < 2; j++) {
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M[i][j] = H[i][j] / xmax;
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}
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}
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}
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b = -M[0][0] - M[1][1];
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c = M[0][0] * M[1][1] - M[1][0] * M[1][0];
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root1 = -.5 * (b + sign(b) * sqrt(b * b - 4 * c));
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root2 = c / root1;
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root1 *= xmax;
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root2 *= xmax;
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*eval1 = min(root1, root2);
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*eval2 = max(root1, root2);
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}
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/* Solve for eigenvector of SPD 2x2 matrix, with given eigenvalue. */
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void eigenvec2(double A[2][2], /* matrix */
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double eval, /* eigenvalue */
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double evec[2], /* eigenvector returned */
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double *res /* normalized residual */
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)
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{
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double norm; /* norm of eigenvector */
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double res1, res2; /* components of residual vector */
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int i; /* loop counter */
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if (fabs(A[0][0] - eval) > fabs(A[1][1] - eval)) {
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evec[0] = -A[1][0];
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evec[1] = A[0][0] - eval;
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}
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else {
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evec[0] = A[1][1] - eval;
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evec[1] = -A[1][0];
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}
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/* Normalize eigenvector and calculate a normalized eigen-residual. */
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norm = sqrt(evec[0] * evec[0] + evec[1] * evec[1]);
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if (norm == 0) {
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evec[0] = 1;
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evec[1] = 0;
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norm = 1;
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}
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for (i = 0; i < 2; i++) {
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evec[i] /= norm;
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}
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res1 = (A[0][0] - eval) * evec[0] + A[1][0] * evec[1];
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res2 = A[1][0] * evec[0] + (A[1][1] - eval) * evec[1];
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*res = sqrt(res1 * res1 + res2 * res2);
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res1 = fabs(A[0][0]) + fabs(A[1][0]);
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res2 = fabs(A[1][1]) + fabs(A[1][0]);
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*res /= max(res1, res2);
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}
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